Composite Structures 66 (2004) 277–285

www.elsevier.com/locate/compstruct

The finite element analysis of composite laminates and shellstructures subjected to low velocity impact

Shiuh-Chuan Her *, Yu-Cheng Liang

Department of Mechanical Engineering, Yuan-Ze University, 135, Yuan-Tung Road, Chung-Li, Tao-Yuan Shian, Taiwan

Available online 5 June 2004

Abstract

In this investigation, the composite laminate and shell structures subjected to low velocity impact are studied by the ANSYS/LS-

DYNA finite element software. The contact force is calculated by the modified Hertz contact law in conjunction with the loading

and unloading processes. In the case of composite laminate, the impact-induced damage including matrix cracking and delamination

are predicted by the appropriated failure criteria and the damaged area are plotted. Two types of shell structure, cylindrical and

spherical shells, are considered in this paper. The effects of various parameters, such as shell curvature, clamped or simple supported

boundary conditions and impactor velocity are examined through the parametric study. Numerical results show that structures with

greater stiffness, such as smaller curvature and clamped boundary condition, result to a larger contact force and a smaller deflection.

The impact response of the structure is proportional to the impactor velocity.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: Finite element; Composite laminate; Shell structure; Impact; Contact force

1. Introduction

Advanced composite structures have been used

widely in many applications such as aerospace, sport

equipments, pressure vessels and automobile parts. It is

well known that composites are very suspectible to

transverse impact. Impact-induced damage may arise

during manufacture, maintenance and service operation.Low velocity impact could cause significant damage, in

terms of matrix cracking and delamination. Such dam-

age is very difficulty to detect by naked eye and can lead

to severe reductions in the stiffness and strength of the

structures. C scan and X-ray are the most popular

nondestructive testing methods to inspect the damage.

The behavior of composite structures subjected to

low velocity impact has been studied by numerousresearchers, including experimental, numerical and

analytical works. Most of the published literatures fo-

cused the impact analysis on flat plates [1–10]. Only a

few researches have been studied the low velocity impact

of laminate shells [11,12]. Analytical solutions for the

impact response of laminate plates are presented by

*Corresponding author. Tel.: +886-3-4638800x451; fax: +866-3-

455-8013.

E-mail address: mesch@saturn.yzu.edu.tw (S.-C. Her).

0263-8223/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compstruct.2004.04.049

Christorforou and Swanson [1], Cairns and Lagace [2],

and Prasad et al. [3]. A number of researchers have

deployed the finite element method for the solution of

impact on composite laminates [4–10]. In Ref. [8] the

authors have used a finite element formulation based on

the Saner’s shell theory to study the impact response and

damage of laminated cylindrical composite shells. While

in Ref. [11], the authors have adopted a 3-D brick ele-ment to investigate the effect of curvature on the dy-

namic response and impact-induced damage in

composite structures. By employing Disciuva’s com-

posite laminate theory with Hashin’s failure criterion,

Wang and Yew [12] calculated the distribution of

damage in each layer under the transverse impact.

Pierson and Vaziri [13] presented an analytical model to

predict the low velocity impact response of simple sup-ported composite laminates. Chun and Lam [14] pro-

posed a numerical method derived by Lagrange’s

principle and Hertzian contact law for the calculation of

dynamic response of laminated composite plates. A

hybrid stress finite element method was employed by

Goo and Kim [15] to simulate the dynamic behavior of

composite laminates under the low velocity impact.

In the present investigation, the ANSYS/LS-DYNAfinite element software is used to calculate the tran-

sient response of the impact on composite laminates,

278 S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285

cylindrical and spherical shells. Deflection and contact

force are the major concerns in the impact response. A

modified Hertzian contact law for loading and unload-

ing processes during the impact period is adopted topredict the contact force. The numerical results are

compared with those existing literatures. The objective

of this research is to study the influence of the shell

curvature, clamped or simple supported boundary con-

dition, impactor velocity on the impact response of the

composite structures. Contact force and center deflec-

tion are presented for various parameters including shell

curvature, boundary condition and impactor velocity.

2. Contact force

The duration of an impact between two bodies occurs

at a very short of period, normally within a few micro

seconds. The transient response of the impact is inves-

tigated on the basis of the following assumptions:

(1) frictionless between the impactor and compositestructure;

(2) neglecting the damping affect in the composite struc-

ture;

(3) ignoring the gravity force during the impact period;

(4) rigid body for the impactor.

Contact force is the most important concern in the

impact analysis. In this study, the contact force is cal-culated, according to the loading and unloading pro-

cesses. During the loading phase, the contact force

follows the Hertzian contact law, and an expression

proposed by Tan and Sun [16] is adopted for the

unloading. These relations are given as

loading Fc ¼ ka1:5 ð1aÞ

unloading Fc ¼ Fma � a0am � a0

� �2:5ð1bÞ

where a denotes the indentation can be calculated by thedifference of the deflections between the composite

structure wsðtÞ and impactor wiðtÞa ¼ wiðtÞ � wsðtÞand k is the modified Hertzian contact stiffness which isdefined for a composite laminate, cylindrical shell and

spherical shell as follows [8]:

for cylindrical shell kcyl ¼4

3

½1=ri þ 1=2rcyl��0:5

½ð1� v2i Þ=Ei þ 1=E2�

for spherical shell ksph ¼4

3

½1=ri þ 1=rsph��0:5

½ð1� v2i Þ=Ei þ 1=E2�where E2 is the elastic modulus transverse to the fiberdirection and ri, vi, Ei are the radius, Poisson’s ratio andelastic modulus of the impactor, respectively. In the

unloading, Fm is the maximum contact force reached

during the impact, am is the maximum indentation

which corresponds to Fm and a0 is the permanent

indentation from the loading/unloading cycle. Expres-sions for the permanent indentation are [17]

for am < acr a0 ¼ 0

for am P acr a0 ¼ am 1

"� acr

am

� �2:5#

where acr is the critical indentation has been taken to be0.0083 mm for graphite/epoxy composite laminates [17].

3. Verification of ANSYS/LS-DYNA

LS-DYNA is a general purpose transient dynamicfinite element program, specializes in contact related

problems such as impact and metal forming. ANSYS

adapts the LS-DYNA as the solver for the impact

problems, however, retains its own pre and post pro-

cesses formed the ANSYS/LS-DYNA. To solve the

impact problems by LS-DYNA, the required input data

can be classified into the following three categories:

1. Material properties: identified the material properties

for the impactor and target object, can be a rigid

body, isotropic material or composite material.

2. Initial and boundary conditions: specified the initial

conditions for the impactor such as impact velocity,

acceleration; boundary conditions for the target ob-

ject such as clamped or simple support.

3. Contact conditions: defined the type of contact andfriction coefficient, there are 18 different types of con-

tact can be chosen to accurately represent the physi-

cal model, among them surface to surface (STS)

and node to surface (NTS) are the most common use.

To verify the accuracy of LS-DYNA, a steel plate

impacted by a rigid ball is examined and compared with

literature result [18]. The Young’s modulus and Pois-son’s ratio of the steel plate are 200 GPa and 0.3,

respectively. The mass, radius and velocity of the

impactor are 0.0329 kg, 10 mm and 1 m/s, respectively.

The plate with length 200 mm, width 200 mm and

thickness 8 mm is clamped along the four edges. Three

different types of mesh using solid elements (SOLID

164) are proposed to conduct the convergence test.

Mesh 1 shows in Fig. 1 with 20 (length) · 20 (width) ·2 (height) ¼ 800 elements in plate and 32 elements in

impactor. Mesh 2 shows in Fig. 2 with 40 (length)· 40(width) · 2 (height) ¼ 3200 elements in plate and 32

elements in impactor. Mesh 3 shows in Fig. 3 with 80

(length) · 80 (width) · 2 (height) ¼ 12,800 elements in

plate and 256 elements in impactor. LS-DYNA is

capable of calculating the transient responses and pro-

Fig. 1. Finite element mesh 1 (20· 20 · 2).

Fig. 2. Finite element mesh 2 (40· 40 · 2).

Fig. 3. Finite element mesh 3 (80· 80 · 2).

Fig. 4. Contact force compared with Karas [18] with mesh 1.

Fig. 5. Contact force compared with Karas [18] with mesh 2.

Fig. 6. Contact force compared with Karas [18] with mesh 3.

S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285 279

vides the displacements and stresses distributions for

both impactor and plate. Thus, one can substitute the

impactor displacements, wiðtÞ and plate displacement

wsðtÞ at the impact points into Hertzian contact law Eq.(1a), to determine the contact force. Figs. 4–6 shows the

results of contact force associated with mesh 1, 2, and 3,

respectively. As shown from the figures, the numericalresults obtained by ANSYS/LS-DYNA can converge to

the analytical solution Kara [18], upon the mesh being

refined.

To demonstrate the capability of LS-DYNA software

in composite structure, the T300/934 [O/)45/45/90]2sgraphite/epoxy composite laminate subjected to low

velocity impact is investigated. The length, width and

thickness of the laminate are 76.2, 76.2 and 2.54 mm,respectively. The material properties of the composite

lamina are listed in Table 1 [6]. Impactor velocity, radius

and density are 25.4 m/s, 6.35 mm and 2800 kg/m3,

respectively. In the case of composite material, the

contact force is calculated by Eqs. (1a) and (1b),

according to the loading and unloading processes. Figs.

7 and 8 show the results of contact force with clamped

and simple supported boundary conditions, respectively.

Table 1

Material properties of T300/934 [6]

Exx

(GPa)

Eyy

(GPa)

Gxy

(GPa)

Vxy Vyz Density q(kg/m3)

145.54 9.997 5.689 0.3 0.3 1535.7

Fig. 7. Contact force T300/934 composite laminate with clamped

boundary condition.

Fig. 8. Contact force T300/934 composite laminate with simply sup-

ported boundary condition.

280 S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285

Excellent agreement can be found between the LS-

DYNA results and Wu and Chang [6].

Table 2

Material properties of T300/976 [7]

Exx

(GPa)

Eyy

(GPa)

Gxy

(GPa)

Gyz

(GPa)

Vxy Uyz Density q(kg/m3)

156 9.09 6.96 3.24 0.228 0.4 1540

Table 3

Strength of T300/976 [7]

Longitudinal tension Xt (MPa) 1520

Longitudinal compression Xc (MPa) 1590

Transverse tension Yt (MPa) 45

Transverse compression Yc (MPa) 252

Ply longitudinal shear Si (MPa) 105

4. Failure analysis

Impact induced damage is a very complicated phe-

nomenon. It requires a understanding of the basicmechanics and damage mechanism. Choi and Chang [7]

had investigated the impact damage by using a line-nose

impactor. Based on the previous studies, Choi and

Chang [7] summarized the impact damage mechanism as

follows:

1. Intraply matrix cracks due to shear or bending initi-

ate the damage.2. These matrix cracks propagate into the nearby inter-

face and cause the delamination between dissimilar

plies.

3. A shear matrix crack located in the inner plies of the

laminate can generate a substantial delamination.

4. A bending matrix crack located at the surface ply

generates a delamination along the first interface of

the cracked ply.

Although the damage mechanism of point-nose im-

pact is much more complicated than line-nose impact,

previous observations regarding the damage process is

still applicable. The sequence of impact damage incomposite laminate can be classified into two stages: (1)

bending or shear stresses initiate the micro cracks in

matrix, (2) propagation of the micro cracks into the

nearby interface yields to the delamination. Thus, in

order to predict the impact damage, two failure criteria

are proposed. Matrix cracking criterion is used to pre-

dict the initiation of damage, and delamination criterion

is adopted to estimate the damaged area. In this study,the failure criteria suggested by Choi and Chang [7] are

adopted and expressed as follows:

Matrix cracking criterion

n�ryy

nY

!2

þn�ryz

nSi

!2

¼ e2M eM P 1 failure ð2Þ

nY ¼ nYt if ryy P 0; nY ¼ nYc if ryy < 0

Delamination criterion

Da

n�ryz

nSi

!224 þ

nþ1�rxz

nþ1Si

!þ

nþ1�ryy

nþ1Y

!235 ¼ e2D

eD P 1 failure ð3Þnþ1Y ¼ nþ1Yt if ryy P 0; nþ1Y ¼ nþ1Yc if ryy < 0

The details of these criteria are given in the reference

cited above.

To verify the ANSYS/LS-DYNA in predicting the

impact damage, T300/976 graphite epoxy composite

were used for the study. The material properties and

strength of T300/976 are listed in Tables 2 and 3 [7],

respectively. Two types of ply orientation, [03/903/03/903/03] thickness 2.16 mm and [04/454/)454/904/)454/454/04]thickness 4.03 mm, are investigated. The length and

width of the specimen are 10 and 7.6 cm, respectively.

The specimen is clamped along the two parallel edges

and free for the other two edges as shown in Fig. 9. The

composite laminate is impacted by a steel ball with ra-

Fig. 9. Specimen used for failure analysis.

Fig. 10. Delamination area of T300/976 ½03=903=03=903=03� subjectedto 3.22, 4.0 and 6.7 m/s impact velocity.

S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285 281

dius of 0.635 cm at the center of the specimen. The

stresses were obtained by ANSYS/LS-DYNA finite

element software, and then substituted into the failurecriteria Eqs. (2) and (3) to determine the impact damage.

½03=903=03=903=03�

Various velocities were imposed to investigate the

effect of the impact velocity on the damage. It was foundthat there was no matrix crack or delamination when the

impact velocity was lower than 3 m/s. It shows that there

exists an impact velocity threshold for the laminate. Fig.

10 shows the delamination region of the composite

laminate subjected to an impact at three different impact

velocities. The dark area in the figure indicates the

location where the stresses were calculated by ANSYS-

LS/DYNA and satisfied the delamination criterion. Thedamaged area is heavily related to the impact velocity.

Multiple interfacial delaminations were found when the

impact velocity was greater than 3.0 m/s. The matrix

cracking at the bottom 0� plies was the first failure modeto be detected due to the bending stress. Then, a

delamination at the last interface between 903/03 ply

groups was predicted after the matrix cracking. Fol-

lowing that, the matrix cracking was also predicted inthe inner 90� and 0� groups which initiated the secondand third delaminations at the second and third inter-

faces. No matrix cracking was found at the top surface,

thus, there was no delamination at the first interface.

Fig. 10 shows the overall projected delamination area.

The predicted delaminations are correlated well with

Choi and Chang [7].

½04=454=�454=904=�454=454=04�

The quasi-isotropic laminate was tested at the impact

velocity of 7.8 m/s. The delamination at each interface is

shown in Fig. 11, except the second interface between

45� and )45� ply groups measured from the top surface.The first delamination was initiated at the last interface

between 454/04 ply groups, and appeared to be the

largest area. Delaminations with relatively smaller sizes

were also found at other interfaces except the second

interface, where no delamination was predicted. It seems

that the first delamination governed the overall delam-

ination size and was more sensitive to the impact

velocity than the other delaminations. It is interesting to

see that the delamination shown in Fig. 11 is oriented

itself along the fiber direction of the bottom ply group of

the delaminated interface.

5. Impact analysis of laminated shells

A doubly curved laminated shell structure subjected

to an impact by a steel ball is shown Fig. 12. The curves

of the shell structure are represented by radii of R1 andR2.

Fig. 12. Laminated shell structure geometry [8].

Fig. 11. Delamination area at each interface of T300/976 ½04=454=454 � 904=� 454=454=04�.

282 S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285

The numerical examples are considered to demon-

strate the capability of ANSYS/LS-DYNA on the im-

pact analysis of a laminated shell structure. A variety of

examples are presented to study the impact responses.

The parameters included in this study are the curvature

of the shell, boundary condition and the impact velocity.The composite material properties AS/H3501 are show

in Table 4 [8]. The lay up for the laminated shell is a four

layer symmetric cross ply with stacking sequence [0/90/

90/0] and thickness 2.54 mm. The impactor is a steel ball

with radius of 6.35 mm and density of 7870 kg/m3. Two

special types of shell structure (cylinder and sphere) are

considered in this study. The geometric properties used

are a ¼ b ¼ 25:4 mm, for a cylindrical shell R1 ¼ 1 andfor a spherical shell R1 ¼ R2 ¼ R. The finite elementmesh is shown in Fig. 13.

Table 4

Material properties of AS/H3501 [8]

Exx

(GPa)

Eyy

(GPa)

Gxy

(GPa)

Gyz

(GPa)

Vxy Density q(kg/m3)

144.8 9.65 7.10 5.92 0.3 1389.2

Fig. 13. Finite element mesh for shell structure.

Fig. 14. Contact force for different radius of cylindrical shell.

Fig. 15. Contact force for different radius of spherical shell.

Fig. 16. Central deflection for different radius of cylindrical shell.

Fig. 17. Central deflection for different radius of spherical shell.

Fig. 18. Contact force of cylindrical shell with clamped and simply

supported boundary conditions.

S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285 283

Fig. 14 shows the effect of the ratio of the radius to

arc length R=a on the contact force for a cylindrical

shell. The impactor velocity is 30 m/s and the shell is

clamped. For the three ratios R=a, the contact force isvirtually the same during the first contact. However,

there is a small difference in the second contact, the

contact force occurs earlier and for a longer period time

when the radius of cylinder is decreasing. This may be

due to the stiffening effect on the cylinder as the radius is

decreasing, results to a higher natural frequencies and

earlier contact. The contact force shown in Fig. 14 is in

good agreement with the results presented in Ref. [8].Fig. 15 shows the effect of the ratio R=a on the contactforce for a spherical shell. The trend of contact force for

the spherical shell is similar to the cylindrical shell. Figs.

16 and 17 show the central deflection of the cylindrical

and spherical shell, respectively.

Fig. 19. Contact force of spherical shell with clamped and simply

supported boundary conditions.

Fig. 20. Contact force of cylindrical shell subjected to different impact

velocity.

Fig. 21. Contact force of spherical shell subjected to different impact

velocity.

Fig. 22. Central deflection of cylindrical shell subjected to different

impact velocity.

Fig. 23. Central deflection of spherical shell subjected to different

impact velocity.

284 S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285

A comparison between clamped and simply sup-

ported boundary conditions for a cylindrical and

spherical shell is shown in Figs. 18 and 19, respectively.

The velocity of impactor is 30 m/s and the ratio of radius

to arc length R=a is equal to 5. The second contact forthe clamped boundary condition occurs earlier than the

simply supported boundary condition. The earlier con-

tact is due to the stiffer boundary condition on theclamped edges.

The effect of impact velocity on the contact force is

shown in Figs. 20 and 21 for a cylindrical and spherical

shell, respectively. The ratio R=a is 5 and boundary

condition is clamped. The contact force is increased

proportion to the impact velocity, while the contact

period is virtually unchanged. Figs. 22 and 23 show the

central deflection of the cylindrical and spherical shell,

respectively.

6. Conclusions

The composite laminated plate and shell structuressubjected to low velocity impact have been analyzed

using ANSYS/LS-DYNA finite element software. The

impact responses are presented for the contact force and

central deflection. The numerical results are in good

agreement with the results found in the literatures. The

results show that the contact force is proportion to the

impactor velocity. However, the contact period is

dependent on the stiffness of the laminated structuresuch as the curvature and boundary condition.

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